There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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The concept of mind

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

Motivated by the notion of generalized fuzzy graphs proposed by Samanta et al.[40] and the notion of single valued neutrosophic graphs proposed by Broumi et al.[30]. In this paper, we define the concept of generalized single valued neutrosophic graphs of first type ( GSVNG-1) and presented a matrix representation for it and studied few properties of this new concept. The concept of GSVNG is a generalization of generalized fuzzy graphs (GFG1).

Generalized Single Valued Neutrosophic Graphs of First Type

Recently, single valued neutrosophic sets and interval valued neutrosophic sets have received great attention among the scholars and have been applied in many applications. These two concepts handle the indeterminacy and consistent information existing in real-life problems. In this chapter, a new Python toolbox is proposed under neutrosophic environment, which consists of some Python code for single valued neutrosophic matrices and interval valued neutrosophic matrices. Some definitions of interval neutrosophic vague set such as union, complement, and intersection are presented. Furthermore, the related examples are included.

A Novel Python Toolbox for Single and Interval-Valued Neutrosophic Matrices

As an expansion of 2-tuple linguistic intuitionistic fuzzy set, the newly developed 2-tuple linguistic neutrosophic set (2-TLNS) is more satisfactory to define decision maker’s assessment information in decision-making problems. 2-TLN aggregation operators are of great significance in multiple attribute group decision making (MAGDM) problems with a 2-tuple linguistic environment. Therefore, in this paper, our main contribution is to develop novel 2-TLN power Heronian aggregation (2-TLNPHM) operators. First, we develop new operational laws established on Dombi T-norm (DTN) and Dombi T-conorm (DTCN). Second, Taking full advantages of the power average (PA) operator and Heronian mean (HM) operator, we develop some new novel power Heronian mean operator and discuss its related properties and special cases. The main advantages of developed aggregation operators are that they not only remove the effect of awkward data which may be too high or too low but also have a good capacity to model the extensive correlation between attributes, making them more worthy for successfully solving more and more complicated MAGDM problems. Thus, we develop a new algorithm to handle MAGDM based on developed aggregation operators. Finally, we apply the proposed method and algorithm to risk assessment for the construction of engineering projects to show the efficiency of the developed method and algorithm. The dominant novelties of this contribution are triplex. First, new operational laws are proposed for 2-TLNNs. Second, novel 2-TLNPHM operators are developed. Third, a new approach for 2-tuple linguistic neutrosophic MAGDM is developed.

/pdf/multiple-attribute-group-decision-making-based-on-2-tuple-3k4dib4y64.pdf

Multiple Attribute Group Decision Making Based on 2-Tuple Linguistic Neutrosophic Dombi Power Heronian Mean Operators

In this study, the neutrosophic triplet G-module is introduced and the properties of neutrosophic triplet G-module are studied. Furthermore, reducible, irreducible, and completely reducible neutrosophic triplet G-modules are defined, and relationships of these structures with each other are examined. Also, it is shown that the neutrosophic triplet G-module is different from the G-module.

https://www.mdpi.com/2227-7390/6/4/53/pdf

Neutrosophic Triplet G-Module

In this paper, (1) one simplified the standard TOPSIS to new Multi-Criteria Decision-Making (MCDM) called Simplified-TOPSIS. Simplified-TOPSIS gives the same results and simplifies the calculation of the classical TOPSIS. An example is presented distinctions between Simplified-TOPSIS and classical TOPSIS are underlined. (2) extend the new Simplified-TOPSIS method to Neutrosophic-simplified-TOPSIS using single valued Neutrosophic information. An example showing the interest of Neutrosophic-simplified-TOPSIS to manipulate the uncertainty linked to information presented in Multi-Criteria Decision-Making.

/pdf/neutrosophic-simplified-topsis-multi-criteria-decision-2r2jpxj27u.pdf

Florentin Smarandache

Papers

Generalized Single Valued Neutrosophic Graphs of First Type

A Novel Python Toolbox for Single and Interval-Valued Neutrosophic Matrices

Multiple Attribute Group Decision Making Based on 2-Tuple Linguistic Neutrosophic Dombi Power Heronian Mean Operators

Neutrosophic Triplet G-Module

Neutrosophic-Simplified-Topsis. Multi-Criteria Decision-Making Using Combined Simplified-Topsis Method and Neutrosophics